It is known that moiré tomography is applicable in widely changed flow fields and not sensitive to heavy vibrative conditions. So a new algebraic iterative algorithm developed from the essence of moiré deflectometry is presented to reconstruct three-dimensional flow fields. The algorithm is demonstrated by mapping a double-hump simulated temperature field by projections with 6 directions, 12 directions and 12 directions with Gaussian error added separately. Under same conditions, two other available tomography reconstruction algorithms, the filter back-projection algorithm and the algebraic reconstruction algorithm with integral operation along the deflectometry-projection data, are used to reconstruct the field. A simulation with an opaque is also made with the new algorithm. The reconstruction results show the new algorithm not only has strong ability of noise immunity, but also can handle reconstructions with incomplete data quite well.